Kilometer Run

The Huffingdale All Boys School has produced a comprehensive set of running standards for young boys. These standards are based on data from young boys attending Huffingdale in good health conditions - as determined by a physician. The table displays the percentile distribution of time on a kilometer run for Huffingdale students at grade levels 1 through 5 according to the Huffingdale model. In a model population -- a large population of young students grade 1 through 5 that conforms to the Huffingdale running standards -- for n=5, 15, 50, 85, and 95, the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent, and faster than or equal to (100 - n) percent, of running times for students of that grade level.

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Height

The graph shows the percentile distribution of height, in centimeters, for running times from 500 to 700 seconds, according to the Huffingdale model. In a model population, for n=5, 15, 50, 85, and 95, the nth percentile in height for a given running time is the unique height among boys of that running time that is taller than or equal to n percent, and shorter than or equal to (100-n) percent, of heights of boys of that running time.  

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For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.


Yes No
If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.
If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.
If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.
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